The supply and demand curves for a product have equations and , respectively, with equilibrium at . Suppose an artificially high price of is imposed, with the resulting consumer demand of . Which of the following is a formula for the change in total gains from trade caused by the artificial price?

Question

The supply and demand curves for a product have equations  and  , respectively, with equilibrium at  . Suppose an artificially high price of  is imposed, with the resulting consumer demand of  . Which of the following is a formula for the change in total gains from trade caused by the artificial price?

Quizplus · Accepted Answer

Total gains from trade refer to the sum of consumer surplus and producer surplus. 
Before the artificial price is imposed, the equilibrium price is 11eb69ff_fea9_cd6a_af94_4fb511e7ff84_TB8190_11, and the equilibrium quantity is 11eb69ff_fea9_4c4b_af94_eb1f11555e69_TB8190_11. 
At this equilibrium point, the consumer surplus is the area below the demand curve and above the equilibrium price. Using the equation for the demand curve, we can find that consumer surplus is: 
CS = (1/2) * (11eb69ff_fea9_cd69_af94_975611f2dc42_TB8190_11 - 11eb69ff_fea9_cd6b_af94_4c5d80ef2a6c_TB8190_11) * 11eb69ff_fea9_4c4b_af94_eb1f11555e69_TB8190_11 = 11eb69ff_fea9_cd6d_af94_63f2b2a70440_TB8190_11

Similarly, producer surplus is the area below the equilibrium price and above the supply curve. Using the equation for the supply curve, we can find that producer surplus is: 
PS = (11eb69ff_fea9_cd6b_af94_4c5d80ef2a6c_TB8190_11 - 11eb69ff_fea9_ca9b_af94_e727dcc8fd2d_TB8190_11) * 11eb69ff_fea9_4c4b_af94_eb1f11555e69_TB8190_11 = 11eb69ff_fea9_f47c_af94_e9b7aa9d6546_TB8190_11

Total gains from trade are the sum of consumer surplus and producer surplus: 
TGT = 11eb69ff_fea9_cd6d_af94_63f2b2a70440_TB8190_11 + 11eb69ff_fea9_f47c_af94_e9b7aa9d6546_TB8190_11 = 11eb69ff_fea9_f47e_af94_f5c6a5ce28aa_TB8190_11

After the artificial price of 11eb69ff_fea9_cd6b_af94_11213d087954_TB8190_11 is imposed, the quantity demanded by consumers is 11eb69ff_fea9_f47c_af94_6123337f5bf0_TB8190_11. This is greater than the quantity supplied by producers, which remains at 11eb69ff_fea9_4c4b_af94_eb1f11555e69_TB8190_11, resulting in a shortage of goods. The change in total gains from trade is the difference between the total gains from trade at the equilibrium point and the total gains from trade with the artificial price: 
Change in TGT = TGT at equilibrium - TGT with artificial price = (11eb69ff_fea9_cd6d_af94_63f2b2a70440_TB8190_11 + 11eb69ff_fea9_f47c_af94_e9b7aa9d6546_TB8190_11) - (11eb69ff_fea9_6fea_af94_8bf918c48d1d_TB8190_11 + 11eb69ff_fea9_6ef0_af94_58a3407a124d_TB8190_11) = 11eb69ff_fea9_f47e_af94_f5c6a5ce28aa_TB8190_11

Therefore, the answer is B.

The Supply and Demand Curves for a Product Have Equations